Stock Analysis on Net
Stock Analysis on Net
Microsoft Excel LibreOffice Calc

3M Co. (NYSE:MMM)

Capital Asset Pricing Model (CAPM)

Intermediate level

Rates of Return

3M Co., monthly rates of return

Microsoft Excel LibreOffice Calc
3M Co. (MMM) Standard & Poor’s 500 (S&P 500)
t Date PriceMMM,t1 DividendMMM,t1 RMMM,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2016 $151.00 1,940.24
1. Feb 29, 2016 $156.87 $1.11 4.62% 1,932.23 -0.41%
2. Mar 31, 2016 $166.63 6.22% 2,059.74 6.60%
3. Apr 30, 2016 $167.38 0.45% 2,065.30 0.27%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2020 $172.73 $1.47 8.90% 3,621.63 10.75%
59. Dec 31, 2020 $174.79 1.19% 3,756.07 3.71%
Average (R): 0.67% 1.22%
Standard deviation: 5.87% 4.36%
3M Co. (MMM) Standard & Poor’s 500 (S&P 500)
t Date PriceMMM,t1 DividendMMM,t1 RMMM,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2016 $151.00 1,940.24
1. Feb 29, 2016 $156.87 $1.11 4.62% 1,932.23 -0.41%
2. Mar 31, 2016 $166.63 6.22% 2,059.74 6.60%
3. Apr 30, 2016 $167.38 0.45% 2,065.30 0.27%
4. May 31, 2016 $168.32 $1.11 1.22% 2,096.95 1.53%
5. Jun 30, 2016 $175.12 4.04% 2,098.86 0.09%
6. Jul 31, 2016 $178.36 1.85% 2,173.60 3.56%
7. Aug 31, 2016 $179.24 $1.11 1.12% 2,170.95 -0.12%
8. Sep 30, 2016 $176.23 -1.68% 2,168.27 -0.12%
9. Oct 31, 2016 $165.30 -6.20% 2,126.15 -1.94%
10. Nov 30, 2016 $171.74 $1.11 4.57% 2,198.81 3.42%
11. Dec 31, 2016 $178.57 3.98% 2,238.83 1.82%
12. Jan 31, 2017 $174.82 -2.10% 2,278.87 1.79%
13. Feb 28, 2017 $186.35 $1.175 7.27% 2,363.64 3.72%
14. Mar 31, 2017 $191.33 2.67% 2,362.72 -0.04%
15. Apr 30, 2017 $195.83 2.35% 2,384.20 0.91%
16. May 31, 2017 $204.47 $1.175 5.01% 2,411.80 1.16%
17. Jun 30, 2017 $208.19 1.82% 2,423.41 0.48%
18. Jul 31, 2017 $201.17 -3.37% 2,470.30 1.93%
19. Aug 31, 2017 $204.32 $1.175 2.15% 2,471.65 0.05%
20. Sep 30, 2017 $209.90 2.73% 2,519.36 1.93%
21. Oct 31, 2017 $230.19 9.67% 2,575.26 2.22%
22. Nov 30, 2017 $243.14 $1.175 6.14% 2,647.58 2.81%
23. Dec 31, 2017 $235.37 -3.20% 2,673.61 0.98%
24. Jan 31, 2018 $250.50 6.43% 2,823.81 5.62%
25. Feb 28, 2018 $235.51 $1.36 -5.44% 2,713.83 -3.89%
26. Mar 31, 2018 $219.52 -6.79% 2,640.87 -2.69%
27. Apr 30, 2018 $194.39 -11.45% 2,648.05 0.27%
28. May 31, 2018 $197.23 $1.36 2.16% 2,705.27 2.16%
29. Jun 30, 2018 $196.72 -0.26% 2,718.37 0.48%
30. Jul 31, 2018 $212.32 7.93% 2,816.29 3.60%
31. Aug 31, 2018 $210.92 $1.36 -0.02% 2,901.52 3.03%
32. Sep 30, 2018 $210.71 -0.10% 2,913.98 0.43%
33. Oct 31, 2018 $190.26 -9.71% 2,711.74 -6.94%
34. Nov 30, 2018 $207.92 $1.36 10.00% 2,760.17 1.79%
35. Dec 31, 2018 $190.54 -8.36% 2,506.85 -9.18%
36. Jan 31, 2019 $200.30 5.12% 2,704.10 7.87%
37. Feb 28, 2019 $207.39 $1.44 4.26% 2,784.49 2.97%
38. Mar 31, 2019 $207.78 0.19% 2,834.40 1.79%
39. Apr 30, 2019 $189.51 -8.79% 2,945.83 3.93%
40. May 31, 2019 $159.75 $1.44 -14.94% 2,752.06 -6.58%
41. Jun 30, 2019 $173.34 8.51% 2,941.76 6.89%
42. Jul 31, 2019 $174.72 0.80% 2,980.38 1.31%
43. Aug 31, 2019 $161.72 $1.44 -6.62% 2,926.46 -1.81%
44. Sep 30, 2019 $164.40 1.66% 2,976.74 1.72%
45. Oct 31, 2019 $164.99 0.36% 3,037.56 2.04%
46. Nov 30, 2019 $169.77 $1.44 3.77% 3,140.98 3.40%
47. Dec 31, 2019 $176.42 3.92% 3,230.78 2.86%
48. Jan 31, 2020 $158.66 -10.07% 3,225.52 -0.16%
49. Feb 29, 2020 $149.24 $1.47 -5.01% 2,954.22 -8.41%
50. Mar 31, 2020 $136.51 -8.53% 2,584.59 -12.51%
51. Apr 30, 2020 $151.92 11.29% 2,912.43 12.68%
52. May 31, 2020 $156.44 $1.47 3.94% 3,044.31 4.53%
53. Jun 30, 2020 $155.99 -0.29% 3,100.29 1.84%
54. Jul 31, 2020 $150.47 -3.54% 3,271.12 5.51%
55. Aug 31, 2020 $163.02 $1.47 9.32% 3,500.31 7.01%
56. Sep 30, 2020 $160.18 -1.74% 3,363.00 -3.92%
57. Oct 31, 2020 $159.96 -0.14% 3,269.96 -2.77%
58. Nov 30, 2020 $172.73 $1.47 8.90% 3,621.63 10.75%
59. Dec 31, 2020 $174.79 1.19% 3,756.07 3.71%
Average (R): 0.67% 1.22%
Standard deviation: 5.87% 4.36%

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1 Data in US$ per share of common stock, adjusted for splits and stock dividends.

2 Rate of return on common stock of MMM during period t

3 Rate of return on S&P 500 (the market portfolio proxy) during period t


Variance and Covariance

3M Co., calculation of variance and covariance of returns

Microsoft Excel LibreOffice Calc
t Date RMMM,t RS&P 500,t (RMMM,tRMMM)2 (RS&P 500,tRS&P 500)2 (RMMM,tRMMM)×(RS&P 500,tRS&P 500)
1. Feb 29, 2016 4.62% -0.41% 15.66 2.67 -6.46
2. Mar 31, 2016 6.22% 6.60% 30.87 28.93 29.89
3. Apr 30, 2016 0.45% 0.27% 0.05 0.90 0.20
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2020 8.90% 10.75% 67.84 90.91 78.53
59. Dec 31, 2020 1.19% 3.71% 0.28 6.21 1.31
Total (Σ): 1,996.97 1,103.45 1,049.42
t Date RMMM,t RS&P 500,t (RMMM,tRMMM)2 (RS&P 500,tRS&P 500)2 (RMMM,tRMMM)×(RS&P 500,tRS&P 500)
1. Feb 29, 2016 4.62% -0.41% 15.66 2.67 -6.46
2. Mar 31, 2016 6.22% 6.60% 30.87 28.93 29.89
3. Apr 30, 2016 0.45% 0.27% 0.05 0.90 0.20
4. May 31, 2016 1.22% 1.53% 0.31 0.10 0.17
5. Jun 30, 2016 4.04% 0.09% 11.39 1.27 -3.81
6. Jul 31, 2016 1.85% 3.56% 1.40 5.48 2.77
7. Aug 31, 2016 1.12% -0.12% 0.20 1.80 -0.60
8. Sep 30, 2016 -1.68% -0.12% 5.50 1.81 3.15
9. Oct 31, 2016 -6.20% -1.94% 47.17 10.00 21.72
10. Nov 30, 2016 4.57% 3.42% 15.22 4.83 8.57
11. Dec 31, 2016 3.98% 1.82% 10.96 0.36 1.99
12. Jan 31, 2017 -2.10% 1.79% 7.65 0.32 -1.57
13. Feb 28, 2017 7.27% 3.72% 43.58 6.25 16.50
14. Mar 31, 2017 2.67% -0.04% 4.03 1.59 -2.53
15. Apr 30, 2017 2.35% 0.91% 2.84 0.10 -0.52
16. May 31, 2017 5.01% 1.16% 18.89 0.00 -0.27
17. Jun 30, 2017 1.82% 0.48% 1.33 0.55 -0.85
18. Jul 31, 2017 -3.37% 1.93% 16.30 0.51 -2.89
19. Aug 31, 2017 2.15% 0.05% 2.20 1.36 -1.73
20. Sep 30, 2017 2.73% 1.93% 4.27 0.50 1.47
21. Oct 31, 2017 9.67% 2.22% 81.01 1.00 8.99
22. Nov 30, 2017 6.14% 2.81% 29.93 2.52 8.69
23. Dec 31, 2017 -3.20% 0.98% 14.91 0.06 0.91
24. Jan 31, 2018 6.43% 5.62% 33.21 19.34 25.34
25. Feb 28, 2018 -5.44% -3.89% 37.29 26.16 31.24
26. Mar 31, 2018 -6.79% -2.69% 55.58 15.28 29.14
27. Apr 30, 2018 -11.45% 0.27% 146.73 0.90 11.49
28. May 31, 2018 2.16% 2.16% 2.23 0.89 1.41
29. Jun 30, 2018 -0.26% 0.48% 0.85 0.54 0.68
30. Jul 31, 2018 7.93% 3.60% 52.77 5.67 17.30
31. Aug 31, 2018 -0.02% 3.03% 0.47 3.26 -1.24
32. Sep 30, 2018 -0.10% 0.43% 0.59 0.63 0.61
33. Oct 31, 2018 -9.71% -6.94% 107.56 66.59 84.63
34. Nov 30, 2018 10.00% 1.79% 87.07 0.32 5.28
35. Dec 31, 2018 -8.36% -9.18% 81.44 108.11 93.84
36. Jan 31, 2019 5.12% 7.87% 19.86 44.20 29.63
37. Feb 28, 2019 4.26% 2.97% 12.91 3.07 6.30
38. Mar 31, 2019 0.19% 1.79% 0.23 0.33 -0.27
39. Apr 30, 2019 -8.79% 3.93% 89.47 7.35 -25.65
40. May 31, 2019 -14.94% -6.58% 243.66 60.81 121.72
41. Jun 30, 2019 8.51% 6.89% 61.49 32.18 44.48
42. Jul 31, 2019 0.80% 1.31% 0.02 0.01 0.01
43. Aug 31, 2019 -6.62% -1.81% 53.03 9.18 22.06
44. Sep 30, 2019 1.66% 1.72% 0.98 0.25 0.49
45. Oct 31, 2019 0.36% 2.04% 0.09 0.68 -0.25
46. Nov 30, 2019 3.77% 3.40% 9.64 4.77 6.78
47. Dec 31, 2019 3.92% 2.86% 10.57 2.69 5.33
48. Jan 31, 2020 -10.07% -0.16% 115.19 1.91 14.84
49. Feb 29, 2020 -5.01% -8.41% 32.22 92.76 54.67
50. Mar 31, 2020 -8.53% -12.51% 84.56 188.57 126.27
51. Apr 30, 2020 11.29% 12.68% 112.85 131.43 121.78
52. May 31, 2020 3.94% 4.53% 10.74 10.94 10.84
53. Jun 30, 2020 -0.29% 1.84% 0.91 0.38 -0.59
54. Jul 31, 2020 -3.54% 5.51% 17.68 18.40 -18.04
55. Aug 31, 2020 9.32% 7.01% 74.85 33.48 50.06
56. Sep 30, 2020 -1.74% -3.92% 5.80 26.45 12.38
57. Oct 31, 2020 -0.14% -2.77% 0.64 15.89 3.20
58. Nov 30, 2020 8.90% 10.75% 67.84 90.91 78.53
59. Dec 31, 2020 1.19% 3.71% 0.28 6.21 1.31
Total (Σ): 1,996.97 1,103.45 1,049.42

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VarianceMMM = Σ(RMMM,tRMMM)2 ÷ (59 – 1)
= 1,996.97 ÷ (59 – 1)
= 34.43

VarianceS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (59 – 1)
= 1,103.45 ÷ (59 – 1)
= 19.02

CovarianceMMM, S&P 500 = Σ(RMMM,tRMMM)×(RS&P 500,tRS&P 500) ÷ (59 – 1)
= 1,049.42 ÷ (59 – 1)
= 18.09


Systematic Risk (β) Estimation

Microsoft Excel LibreOffice Calc
VarianceMMM 34.43
VarianceS&P 500 19.02
CovarianceMMM, S&P 500 18.09
Correlation coefficientMMM, S&P 5001 0.71
βMMM2 0.95
αMMM3 -0.49%

Calculations

1 Correlation coefficientMMM, S&P 500
= CovarianceMMM, S&P 500 ÷ (Standard deviationMMM × Standard deviationS&P 500)
= 18.09 ÷ (5.87% × 4.36%)
= 0.71

2 βMMM
= CovarianceMMM, S&P 500 ÷ VarianceS&P 500
= 18.09 ÷ 19.02
= 0.95

3 αMMM
= AverageMMM – βMMM × AverageS&P 500
= 0.67%0.95 × 1.22%
= -0.49%


Expected Rate of Return

Microsoft Excel LibreOffice Calc
Assumptions
Rate of return on LT Treasury Composite1 RF 1.94%
Expected rate of return on market portfolio2 E(RM) 11.90%
Systematic risk (β) of 3M Co.’s common stock βMMM 0.95
 
Expected rate of return on 3M Co.’s common stock3 E(RMMM) 11.41%

1 Unweighted average of bid yields on all outstanding fixed-coupon U.S. Treasury bonds neither due or callable in less than 10 years (risk-free rate of return proxy).

2 See details »

3 E(RMMM) = RF + βMMM [E(RM) – RF]
= 1.94% + 0.95 [11.90%1.94%]
= 11.41%